Design and implementation issues for a class of distribution-free Phase II EWMA exceedance control charts

Abstract

Distribution-free (nonparametric) control charts can play an essential role in process monitoring when there is dearth of information about the underlying distribution. In this paper, we study various aspects related to an efficient design and execution of a class of nonparametric Phase II exponentially weighted moving average (denoted by NPEWMA) charts based on exceedance statistics. The choice of the Phase I (reference) sample order statistic used in the design of the control chart is investigated. We use the exact time-varying control limits and the median run-length as the metric in an in-depth performance study. Based on the performance of the chart, we outline implementation strategies and make recommendations for selecting this order statistic from a practical point of view and provide illustrations with a dataset. We conclude with a summary and some remarks.

An assessment for the conditional performance of an support vector data description (SVDD)‐based chart

“…However, in many applications, when the multivariate normality assumption is often questionable or the actual distribution is unknown, these parametric schemes may potentially be (highly) affected. For univariate processes, several studies have shown that a departure from normality severely deteriorates the monitoring properties of schemes based on the normal theory, see Graham et al, 4 Asghari et al, 5 Castagliola et al, 6 Tang et al, 7 and Alevizakos et al 8 This situation is exacerbated for multivariate processes as the multivariate normality is even more uncommon than the univariate one. Therefore, in recent years, a host of nonparametric multivariate SPM schemes have emerged as attractive alternatives to multivariate parametric ones.…”

Distribution‐free double‐sampling precedence monitoring scheme to detect unknown shifts in the location parameter

“…The precedence and exceedance monitoring schemes are a class of nonparametric Phase II monitoring schemes that can be used to monitor the j ‐th order statistic of a continuous process distribution, where is a non‐zero integer; see Chakraborti et al 16 . For memory‐type (i.e., exponentially weighted moving average [EWMA], cumulative sum [CUSUM] and generally weighted moving average [GWMA]) schemes based on the precedence or exceedance statistics, readers need to consult Graham et al., 17–19 Mukherjee et al., 20 Chakraborty et al 21 . and Karakani et al 22 .…”

“…The precedence and exceedance monitoring schemes are a class of nonparametric Phase II monitoring schemes that can be used to monitor the j-th order statistic of a continuous process distribution, where 𝑗 is a non-zero integer; see Chakraborti et al 16 For memory-type (i.e., exponentially weighted moving average [EWMA], cumulative sum [CUSUM] and generally weighted moving average [GWMA]) schemes based on the precedence or exceedance statistics, readers need to consult Graham et al, [17][18][19] Mukherjee et al, 20 Chakraborty et al 21 and Karakani et al 22 For the one-sided basic and weighted precedence schemes, Balakrishnan et al 23 used the Lehmann alternatives approach to formulate exact expressions to calculate some of the run length distribution metrics. For the Shewhart-type schemes, Chakraborti et al 24 reported that the basic Shewhart precedence scheme is slow in detecting small shifts in the process parameter.…”

One-sided precedence monitoring schemes for unknown shift sizes using generalized 2-of-(h+1) and w-of-w improved runs-rules

“…For Case K, see for example, Human et al (2010), Khilare and Shirke (2010), Kritzinger et al (2014), Khilare and Shirke (2015), Patil and Shirke (2017), Pawar et al (2018), etc. For Case U, see for example, Chakraborti and van de Wiel (2008), Chakraborti et al (2009a), Albers and Kallenberg (2008), Graham et al (2017), Malela-Majika et al (2019), etc. In Case U scenario, it is well-known and accepted that there are two distinct phases or stages, namely Phase I (or retrospective phase) and Phase II (or prospective or monitoring phase).…”